Problem: Simplify the following expression and state the condition under which the simplification is valid. $y = \dfrac{n^2 - 16}{n + 4}$
Explanation: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = n$ $ b = \sqrt{16} = 4$ So we can rewrite the expression as: $y = \dfrac{({n} + {4})({n} {-4})} {n + 4} $ We can divide the numerator and denominator by $(n + 4)$ on condition that $n \neq -4$ Therefore $y = n - 4; n \neq -4$